Space of modular forms of level 540, weight 4, and Character 540.i

• Label: 540.4.i
• Level: $540$
• Weight: $4$
• Character orbit: 540.i
• Rep. character: $\chi_{540}(181,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $24$
• Newform subspaces: $3$
• Sturm bound: $432$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 540 = 2^{2} \cdot 3^{3} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	540.i (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 9 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(432\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(540, [\chi])\).

	Total	New	Old
Modular forms	684	24	660
Cusp forms	612	24	588
Eisenstein series	72	0	72

Trace form

\( 24 q + 10 q^{5} + 12 q^{7} + O(q^{10}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(540, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
540.4.i.a	$540$	$4$	540.i	9.c	$3$	$2$	$1$	$31.861$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(0\)	\(-5\)	\(7\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-5\zeta_{6}q^{5}+(7-7\zeta_{6})q^{7}+(-30+30\zeta_{6})q^{11}+\cdots\)
540.4.i.b	$540$	$4$	540.i	9.c	$3$	$8$	$4$	$31.861$	8.0.\(\cdots\).1	None		$2$	$0$	\(0\)	\(0\)	\(-20\)	\(13\)	$2^{2}\cdot 3^{6}$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-5-5\beta _{4})q^{5}+(2\beta _{2}-3\beta _{4}-\beta _{5}+\cdots)q^{7}+\cdots\)
540.4.i.c	$540$	$4$	540.i	9.c	$3$	$14$	$7$	$31.861$	\(\mathbb{Q}[x]/(x^{14} - \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(35\)	\(-8\)	$2^{10}\cdot 3^{17}$	$\mathrm{SU}(2)[C_{3}]$	\(q+(5-5\beta _{7})q^{5}+(-\beta _{7}-\beta _{9})q^{7}+(\beta _{1}+\cdots)q^{11}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(540, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(540, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(9, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(18, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(27, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(36, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(54, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(108, [\chi])\)\(^{\oplus 2}\)